The kinetic energy of an electron, -particle and a proton are given as 4K, 2K and K respectively. The de-Broglie wavelength associated with electron , -particle and the proton are as follows [2023]

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Q.
The kinetic energy of an electron, $α$ -particle and a proton are given as 4K, 2K and K respectively. The de-Broglie wavelength associated with electron $(λ_{e})$ , $α$ -particle $(λ_{α})$ and the proton $(λ_{p})$ are as follows [2023]

1 $λ_{α} = λ_{p} > λ_{e}$

2 $λ_{α} > λ_{p} > λ_{e}$

3 $λ_{α} < λ_{p} < λ_{e}$

4 $λ_{α} = λ_{p} < λ_{e}$

Ans.
(3)

Electron Alpha Proton

Mass: $\frac{m}{1840}$ $4 m$ $m$

Charge: $e$ $2 e$ $e$

Kinetic energy: $4 K$ $2 K$ $K$

$λ = \frac{h}{\sqrt{2 m K}}$ $\frac{h}{\sqrt{2 \cdot (\frac{m}{1840}) \cdot 4 K}}$ $\frac{h}{\sqrt{2.4 m . 2 K}}$ $\frac{h}{\sqrt{2 m K}}$

$λ_{α} < λ_{p} < λ_{e}$

Solution

Q.
The kinetic energy of an electron, $α$ -particle and a proton are given as 4K, 2K and K respectively. The de-Broglie wavelength associated with electron $(λ_{e})$ , $α$ -particle $(λ_{α})$ and the proton $(λ_{p})$ are as follows [2023]

1 $λ_{α} = λ_{p} > λ_{e}$

2 $λ_{α} > λ_{p} > λ_{e}$

3 $λ_{α} < λ_{p} < λ_{e}$

4 $λ_{α} = λ_{p} < λ_{e}$

Ans.
(3)

Electron Alpha Proton

Mass: $\frac{m}{1840}$ $4 m$ $m$

Charge: $e$ $2 e$ $e$

Kinetic energy: $4 K$ $2 K$ $K$

$λ = \frac{h}{\sqrt{2 m K}}$ $\frac{h}{\sqrt{2 \cdot (\frac{m}{1840}) \cdot 4 K}}$ $\frac{h}{\sqrt{2.4 m . 2 K}}$ $\frac{h}{\sqrt{2 m K}}$

$λ_{α} < λ_{p} < λ_{e}$

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	Electron	Alpha	Proton
Mass:	$\frac{m}{1840}$	$4 m$	$m$
Charge:	$e$	$2 e$	$e$
Kinetic energy:	$4 K$	$2 K$	$K$
$λ = \frac{h}{\sqrt{2 m K}}$	$\frac{h}{\sqrt{2 \cdot (\frac{m}{1840}) \cdot 4 K}}$	$\frac{h}{\sqrt{2.4 m . 2 K}}$	$\frac{h}{\sqrt{2 m K}}$

Solution

Q. The kinetic energy of an electron, α-particle and a proton are given as 4K, 2K and K respectively. The de-Broglie wavelength associated with electron (λe), α-particle (λα) and the proton (λp) are as follows [2023]

1 λα=λp>λe

2 λα>λp>λe

3 λα<λp<λe

4 λα=λp<λe

Ans. (3) Electron Alpha Proton Mass: m1840 4m m Charge: e 2e e Kinetic energy: 4K 2K K λ=h2mK h2·(m1840)· 4K h2.4m.2K h2mK λα<λp<λe

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Q.
The kinetic energy of an electron, $α$ -particle and a proton are given as 4K, 2K and K respectively. The de-Broglie wavelength associated with electron $(λ_{e})$ , $α$ -particle $(λ_{α})$ and the proton $(λ_{p})$ are as follows [2023]

1 $λ_{α} = λ_{p} > λ_{e}$

2 $λ_{α} > λ_{p} > λ_{e}$

3 $λ_{α} < λ_{p} < λ_{e}$

4 $λ_{α} = λ_{p} < λ_{e}$

Ans.
(3)

Electron Alpha Proton

Mass: $\frac{m}{1840}$ $4 m$ $m$

Charge: $e$ $2 e$ $e$

Kinetic energy: $4 K$ $2 K$ $K$

$λ = \frac{h}{\sqrt{2 m K}}$ $\frac{h}{\sqrt{2 \cdot (\frac{m}{1840}) \cdot 4 K}}$ $\frac{h}{\sqrt{2.4 m . 2 K}}$ $\frac{h}{\sqrt{2 m K}}$

$λ_{α} < λ_{p} < λ_{e}$